Mirror an object via modifiers on a point(instead of a plane)
Create an empty at the origin of your object.
Rotate it 180&deg; relative to the object's rotation.
Add an Array modifier to your object, and disable all offsets.
Enable Object Offset and select the empty from the list.




Using the Object Offset can be a very powerful tool



Another Solution to this would be to use a linked copy, created with AltD and rotate that 180°. Linked copies share the same mesh.